"Mensuration" question number distribution across years

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Mathematics index on skoool nigeria

WAEC questions for "Mathematics :: Mensuration"

Q1

An empty rectanglar tank is 250cm long and 120cm wide. If 180 litres of water is poured into the tank, calculate the height of the water

A

6.0cm

B

5.5cm

C

5.0cm

D

4.5cm

E

**Answer:** A

Q2

The diagram is a net right rectangular pyramid. Calculate the total surface area.

A

208cm²

B

112cm²

C

92cm²

D

76cm²

E

**Answer:** C

Q3

What is the lenggh of a rectanglar garden whose perimeter is 32cm and area 39cm²?

A

25cm

B

18cm

C

13cm

D

9cm

E

**Answer:** C

Q4

A casting is made up of Copper and Zinc. If 65% of the casting is Zinc and there are 147g of copper, what is the mass of the casting?

A

320g

B

420g

C

520g

D

620g

E

**Answer:** B

Q5

A rectangle has length xcm and width(x-1)cm. If the perimeter is 16cm, find the value of x.

A

3^{1}/_{2}cm

B

4cm

C

4^{1}/_{2}cm

D

5cm

E

**Answer:** C

Q6

In the diagram shows a rectanglar cardboard from which a semi-circle is cut off. Calculate the area of the remaining part.

A

44cm²

B

99cm²

C

154cm²

D

165cm²

E

**Answer:** B

Q7

How many times, correct to the nearest whole number, will a man run round a circular track of diameter 100m to cover a disatnce of 1000m

A

3

B

4

C

5

D

6

E

**Answer:** A

Q8

The diameter of a bicycle wheel is 42cm. If the wheel makes 16 complete revolution, what will be the total distance covered by the wheel? [Take π = ^{22}/_{7}]

A

672cm

B

1056cm

C

2112cm

D

4224cm

E

**Answer:** C

Q9

Calculate, correct to the nearest cm², the area of the trapeziium.

A

27cm²

B

30cm²

C

36cm²

D

37cm²

E

**Answer:** A

Q10

The capacity of a water tank is 1,800 litres. if the tank is in form of a cuboid with base 600 *cm* by 150 *cm*, find the height of the tank.

A

2cm

B

20cm

C

200cm

D

2000cm

E

**Answer:** B

Q11

An arc of a circle subtends and angle of 60° at the centre. if the radius of the circle is 3 cm, find, in terms of π, the length of the arc.

A

πcm

B

2πcm

C

3πcm

D

6πcm

E

**Answer:** A

Q12

A bucket holds 10 litres of water. How many buckets of water will fill a reservoir of the 8m x 7m x 5m. (1 litre = 1000cm³)

A

28

B

280

C

2800

D

28000

E

**Answer:** D

Q13

If the volume of a cube is 343cm³, find the length of its side.

A

3cm

B

6cm

C

7cm

D

8cm

E

**Answer:** C

Q14

In the diagram, **PQRS** is a rhombus. /**PR**/ = 10cm and /**QS**/ = 24cm. Calculate the perimeter of the rhombus.

A

34cm

B

52cm

C

56cm

D

96cm

E

**Answer:** B

Q15

What is the length of an edge of a cube whose total surface area is X cm² and whose volume is ^{X}/_{2} cm³?

A

3

B

6

C

9

D

12

E

**Answer:** A

Q16

If the perimeter of Δ**PQR** in the diagram is 24cm, what is the area of Δ**PRS**?

A

19.5cm²

B

15.0cm²

C

13.0cm²

D

9.3cm²

E

**Answer:** B

Q17

<PQR is a sector of a circle centre O, radius 4cm. If <PQR = 30° find, correct to 3 significant figures, the area of sector <POR. [Take π ^{22}/_{7}]

A

4.19cm^{2}

B

8.38cm^{2}

C

10.5cm^{2}

D

20.9cm^{2}

E

**Answer:** A

Q18

A chord of length 6cm is drawn in a circle of radius 5cm. Find the distance of the chord from the centre of the circle.

A

2.5cm

B

3.0cm

C

3.5cm

D

4.0cm

E

**Answer:** D

Q19

A sector of a circle of radius 14cm containing an angle 60° is folded to form a cone. Calculate the radius of the base of the cone.

A

5^{1}/_{2}cm

B

4^{2}/_{3}cm

C

3^{1}/_{2}cm

D

2^{1}/_{3}cm

E

**Answer:** D

Q20

Find the volume of a solid cylinder with base radius 10cm and height 14cm (Take π = 22/7)

A

220cm³

B

880cm³

C

1400cm³

D

4400cm³

E

**Answer:** D

Q21

PQR is an equilateral triangle with side 2√3 cm. Calculate its height.

A

1.7cm

B

3.0cm

C

3.2cm

D

3.9cm

E

**Answer:** B

Q22

Two circles have radii 16cm and 23cm. What is the difference between their circumferences? (Take π = 22/7)

A

244.92cm

B

149.92cm

C

44.00cm

D

43.96cm

E

**Answer:** C

Q23

The volume of a cylinder is 1200cm³ and the area of its base is 150cm². Find the height of the cylinder.

A

80.00cm

B

8.00cm

C

0.80cm

D

0.08cm

E

**Answer:** B

Q24

In the diagram, O is the centre of the circle and PQ is a diameter. Triangle RSO is an equilateral triangle of side 4cm. Find the area of the shaded region

A

43.36cm²

B

32.07cm²

C

18.21cm²

D

6.93cm²

E

**Answer:** C

Q25

A baker used 40% of a 50kg bag of flour. If 1/8 of the amount used was for the cake, how many kilograms of flour was used for cake?

A

2^{1}/_{2}

B

6^{1}/_{4}

C

15^{5}/_{8}

D

17^{1}/_{2}

E

**Answer:** A

Q26

in the diagram, PQUV, PQTU, QRST are parallelograms. |UV| = 4.8cm and perpendicular distance between PR and VS is 5cm. Calculate the area of quadrilateral PRSV

A

96cm²

B

72cm²

C

60cm²

D

24cm²

E

**Answer:** C

Q27

A conical water-jug is 7cm in diagram and 6cm deep. Find thne volume of water it can hold. [Take π = 22/7]

A

22cm³

B

44cm³

C

77cm³

D

308cm³

E

**Answer:** C

Q28

In the diagram, the two circles have a common centre O. if the area of the larger circle is 100π and that of the smaller circle is 49π, find x.

A

2

B

3

C

4

D

6

E

**Answer:** B

Q29

The wheel of a tractor has a diameter 1.4m. What distance does it cover in 100 complete revolutions? [Take π = 22/7]

A

140m

B

220m

C

280m

D

440m

E

**Answer:** D

Q30

A rectangles carpet 2.5m long and 2.4m wide covers 5% of a rectanglar floor. Calculate the area of the floor.

A

30m²

B

57m²

C

120m²

D

225m²

E

**Answer:** C

Q31

The lenths of the adjacent sides of a right-angled triangle are xcm. If the length of the hypotenuse is √13cm, find the value of x.

A

2

B

3

C

4

D

5

E

**Answer:** B

Q32

What is the diameter of a circle of area 77cm²? (Take π = 22/7)

A

^{√2}/_{7}cm

B

3^{1}/_{2}cm

C

7cm

D

7√2cm

E

**Answer:** D

Q33

What is the total surface area of a closed cylinder of height 10cm and diameter 7cm? (Take π= 22/7)

A

77cm^{2}

B

227cm^{2}

C

297cm^{2}^{}

D

374cm^{2}

E

**Answer:** C

Q34

An arc of a cicle odf radius 14cm subtends angle 300 at the centre. Find the perimeter of the sector formed by the arc (Take π = 22/7)

A

14.67cm

B

42.67cm

C

101.33cm

D

513.33cm

E

**Answer:** C

Q35

The total surface area of the walls of a room, 7m long, 5m wide and xm high is 96m^{2} . Find the value of x.

A

2/3

B

2

C

4

D

8

E

**Answer:** C

Q36

A rectanglear packet has inner dimension 16cm by 12cm by 6cm. How many cubes of suger of side 2cm can be neatly packed into the packet?

A

90

B

144

C

150

D

288

E

**Answer:** B

Q37

XOY is a sector of a circle O of radius 3.5cm which subtends an angle of 114° at the centre. Calculate, in terms of π, the area of the sector.

A

1.4π cm²

B

2.8π cm²

C

4.9π cm²

D

9.8π cm²

E

**Answer:** C

Q38

Find the area of a rectangle of length 4 cm and whose diagonal is 8cm. (Leave your answer in surd form)

A

8√3cm²

B

12√3cm²

C

16√2cm²

D

16√3cm²

E

**Answer:** D

Q39

Calculate the total surface area of a cupboard which measures 12cm by 10cm by 8cm

A

1920cm²

B

592cm²

C

296cm²

D

148cm²

E

**Answer:** B

Q40

What is the volume of a solid cylinder of diameter 7cm and height 7cm? (Take π = ^{22}/_{7})

A

38.5cm³

B

77cm³

C

269.5cm³

D

1078cm³

E

**Answer:** C

Q41

The sides of two cubes are in the ratio 2:5. What is the ratio of their volumes?

A

4:5

B

8:15

C

6:125

D

8:125

E

**Answer:** D

Q42

A pyramid of volume 120cm³ has a rectanguar base which measures 5cm by 6cm. Calculate the height of the pyramid

A

5cm

B

9cm

C

12cm

D

15cm

E

**Answer:** C

Q43

In the diagram /PS/ = 9cm, /QR/ 5cm, <PSR = 63° and <SPQ = PQR = 90°. Find correct to the nearest whole number, the area of the trapezium.

A

55cm²

B

25cm²

C

22cm²

D

13cm²

E

**Answer:** A

Q44

A right circular cone is such that its radius r is twice its height h. Find its volume in terms of h.

A

^{2}/_{3 }πh²

B

^{1}/_{12} πh²

C

^{4}/_{3}πh²

D

^{4}/_{3} πh³

E

**Answer:** D

Q45

The lengths of the parallel sides of a trapezium are 9 cm and 12 cm. If the area of the trapezium is 105 cm², find the perpendicular distance between the parallel sides.

A

5cm

B

7cm

C

10cm

D

15cm

E

**Answer:** C

Q46

The base diameter of a cone is 14cm, and its volume is 462cm². Find its height [Take π = 22/7]

A

3.5cm

B

5cm

C

7cm

D

9cm

E

**Answer:** D

Q47

In the diagram O and O^{I} are the centres of the circles radius 15cm and 8cm respectively. if PQ = 12cm, find OO^{I}

A

8.46cm

B

19.04cm

C

20.81cm

D

26.16cm

E

**Answer:** B

Q48

The volume of a cylinder of radius 14cm is 210cm³. What is the curved surface area of the cylinder?

A

15cm²

B

30cm²

C

616cm²

D

1262cm²

E

**Answer:** B

Q49

In the diagram, QRT is a straight line. If angle PTR = 90°, angle PRT = 60°, angle PQR = 30° and |PQ| = 6√3cm, calculate |RT|

A

0.3cm

B

^{√3}/_{2} cm

C

3cm

D

3√3cm

E

**Answer:** C

Q50

To arrive on schedule, a train is to cover a distance of 60km at 72km/hr. If it strats 10 minute late, at what speed must it move to arrive on schedule?

A

60km/hr

B

80km/hr

C

90km/hr

D

108km/hr

E

**Answer:** C

Q51

A right pyramid is on a square base of side 4cm. The slanting side of the pyramid is 2√3cm. Calculate the volume of the pyramid

A

5^{1}/_{3} cm³

B

10^{2}/_{3} cm³

C

16cm³

D

32cm³

E

**Answer:** B

Q52

A height of a right circular cone is 4cm. The radius of its base is 3cm. Find its curved surface area.

A

9πcm²

B

15πcm²

C

16πcm²

D

20πcm²

E

**Answer:** B

Q53

A chord of length 30cm is 8cm away from the center of the circle. What is the radius of the circle.

A

16cm

B

17cm

C

18cm

D

20cm

E

**Answer:** B

Q54

A sector of a circle radius 14cm subtends an angle of 135° at the centre of the circle. What is the perimeter of the sector? (Take π = 22/7)

A

47cm

B

61cm

C

88cm

D

231cm

E

**Answer:** B

Q55

In the diagram, MN//PQ, /LM/ = 3cm and /LP/ = 4cm. If the area of ΔLMN is 18cm², Find the area of quadrilateral MPQN. The diagram show a trianglar prism of langth 7cm. the right-angleded triangle PQR is a cross-section of the prism. /PR/ = 5cm and /RQ/ = 3cm

A

3cm²

B

6cm²

C

14cm²

D

24cm²

E

**Answer:** C

Q58

A solid cylinder of radius 7cm is 10cm long. Find its total surface area.

A

70πcm²

B

189πcm²

C

210πcm²

D

238πcm²

E

**Answer:** D

Q59

PQRS is a trapezium in which /PS/ = 9cm, /QR/ = 15cm, /PQ/ = 2√3, <PQR = 90° and <QRS = 30°. Calculate the area of the trapezium.

A

24√3 cm²

B

36√3 cm²

C

42√3 cm²

D

72√3 cm²

E

**Answer:** A

Q60

A bivycle wheel of radius 42cm is rolled over a distance of 66 metres. How many revolutions does it makes? [Take π = 22/7]

A

2.5

B

5

C

25

D

50

E

**Answer:** C